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Консультация № 201293
25.07.2021, 13:02
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Найти область сходимости ряда на скрине
Найти область сходимости ряда на скрине
Прикрепленные файлы:
Обсуждение
25.07.2021, 16:47
общий
это ответ
Здравствуйте, oligator.a.y!
Предлагаю Вам следующее решение задачи.
Используем признак Даламбера:
Определим, при каких значениях
этот предел меньше 1: 
откуда 
В этом интервале заданный ряд сходится абсолютно.
При
заданный ряд расходится. Граничные точки 
исследуем особо.
При
ряд имеет вид 
и расходится (не выполняется необходимое условие сходимости). При 
получаем ряд 
для которого не выполняются условия признака Лейбница.
Таким образом, областью сходимости заданного ряда является интервал
Предлагаю Вам следующее решение задачи.
Используем признак Даламбера:
Определим, при каких значениях
этот предел меньше 1: откуда В этом интервале заданный ряд сходится абсолютно.При
заданный ряд расходится. Граничные точки исследуем особо.При
ряд имеет вид и расходится (не выполняется необходимое условие сходимости). При получаем ряд для которого не выполняются условия признака Лейбница.Таким образом, областью сходимости заданного ряда является интервал
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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